Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#393 | C2 |
| prime radical | C22×#67 | C22 |
| hypercenter | #393 | D3 |
| hypocenter | C3 | #2785 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#393 | C2 | semidirect |
| 2. #5231 | C2 | semidirect |
| 3. #5230 | C2 | semidirect |
| 5. #4945 | C2 | semidirect |
| 6. #4669 | C2 | semidirect |
| 7. #4650 | C2 | semidirect |
| 25. #393 | D3 | semidirect |
| 151. C3 | #2785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#393 | 2 |
| #5231 | 2 |
| #5230 | 2 |
| #4959 | 2 |
| #4945 | 2 |
| #4669 | 2 |
| #4650 | 2 |
| #2785 | 3 |